Finite Group Databasebeta

← #34059790

Subgroups — #34059790

Order 19072.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750612C211yesmaximal, characteristic
2#23750599C211yesmaximal, characteristic
3#23749597C211yesmaximal, characteristic
4C2×#14558746C411yescharacteristic, complemented
5C2×#14558745—21no—
6C2×D149⋊C8C411yescharacteristic, complemented
7#18011972C412yescomplemented
8#18011971—21no—
9C22⋊#11924753—21no—
10C22⋊#11924753—21no—
11C2×#14558735C2211yescharacteristic
12#18011867—21no—
13#18011826C411yescharacteristic
14#18011825—21no—
15#99×C149C411yescharacteristic
16#14558746—41no—
17#14558745—22no—
18#14558745—41no—
19D149⋊C8—41no—
20C2×#11924753—21no—
21C2×#11924753—21no—
22C2×#11924753—41no—
23#14558735—41no—
24#14558735—41no—
25C2×Dic298C2×C411yescharacteristic
26C2×C22⋊D149D411yescharacteristic
27C2×C22⋊D149Q811yescharacteristic
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C2×C4×D149C2×C411yescharacteristic
31#14558715—41no—
32C22⋊Dic149—21no—
33C4×Dic149—41no—
34C2×D4×C149C2×C411yescharacteristic
35C22⋊C4×C149—21no—
36#11924753—42no—
37#11924753—41no—
38#11924753—41no—
39C22×D149C4⋊C411yescharacteristic
40Dic298—41no—
41C22⋊D149—41no—
42C22⋊D149—41no—
43C2×Dic149—21no—
44C2×Dic149—21no—
45C2×Dic149—21no—
46C2×Dic149—21no—
47C2×Dic149—41no—
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C4⋊C411yescharacteristic
51C4×D149—21no—
52C4×D149—21no—
53C23×C149C22⋊C411yescharacteristic
54C23×C149C4⋊C411yescharacteristic
55D4×C149—41no—
56C2×C4×C149—41no—
57C2×C4×C149C4211yescharacteristic
58C22×C149—21no—
59C22×C149—21no—
60C22×C149—41no—
61C22×C149—41no—
62C22×C149#9511yescharacteristic
63C2×D149—21no—
64C2×D149—41no—
65C4×C149—21no—
66C4×C149—81no—
67Dic149—21no—
68Dic149—21no—
69Dic149—81no—
70Dic149#9911yescharacteristic
71Dic149#9911yescharacteristic
72C2×C149—21no—
73C2×C149—41no—
74C2×C149—41no—
75C2×C149#34211yescharacteristic
76D149—41no—
77C149#139511yescharacteristic, complemented, Sylow
78#1395—1491nomaximal, Sylow
79#413—1491no—
80#410—1491no—
81#408—1491no—
82C2×#41—1491no—
83C2×M16—2981no—
84C2×M16—1491no—
85C22×C8—1491no—
86#117—2981no—
87#101—1492no—
88#100—2981no—
89#99—2981no—
90#99—1491no—
91#99#1059701011yescharacteristic
92C22⋊C8—2981no—
93C22⋊C8—2981no—
94#41—5961no—
95#41—5961no—
96C2×Q8—1491no—
97C2×D4—1491no—
98C2×D4—1491no—
99C2×D4C2×#1059701011yescharacteristic
100C22×C4—1491no—
101C22×C4—1491no—
102C22×C4—1491no—
103M16—2982no—
104M16—5961no—
105M16—5961no—
106C2×C8—2981no—
107C2×C8—2981no—
108C2×C8—5961no—
109C2×C8—5961no—
110C4⋊C4—5961no—
111C22⋊C4—21no—
112C22⋊C4—2981no—
113C42—5961no—
114C23—1491no—
115C23C22⋊#1059701011yescharacteristic
116C23C4⋊#1059701011yescharacteristic
117Q8—5961no—
118D4—41no—
119D4—5961no—
120D4—5961no—
121C2×C4—41no—
122C2×C4—2981no—
123C2×C4—2981no—
124C2×C4—2981no—
125C2×C4—2981no—
126C2×C4—2981no—
127C2×C4—2981no—
128C2×C4—5961no—
129C2×C4—1491no—
130C2×C4—1491no—
131C2×C4—1491no—
132C2×C4C4×#1059701011yescharacteristic
133C8—5962no—
134C8—5961no—
135C8—5961no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—2981no—
141C22—5961no—
142C22(C2×#10597010)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—2981no—
146C4—2981no—
147C4—1491no—
148C4—1491no—
149C4—11921no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—5961no—
154C2#2375050211yescharacteristic
subgroupG/H
centerC2#23750502
commutatorC2×C4×C149C42
FrattiniC2×D4C2×#10597010
Fitting#99×C149C4
socleC2×C149#342
prime radical, cosocleC2×#14558735C22
hypercenter#99#10597010
hypocenterC149#1395
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#14558746C4semidirect
6. C2×D149⋊C8C4semidirect
7. #18011972C4semidirect
77. C149#1395semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237506122
#237505992
#237495972
#1395149